A simple pendulum of time period 1s and length l is hung from a fixed support at O, such that the bob is at a distance H vertically above A on the ground. The amplitude is θo. The string snaps at θ = θ0/2. Find the time taken by the bob to hit the ground. Also, find the distance from A where bob hits the ground. Assume θ0 to be small so that sin θo, θo and cos θ0 1.

contexto.120

3 years ago

Answer:

At t = t1 and θ= θ₀/a

We have, T = 1 sec

θ₀/2 = θ₀ cos 2π/T t1

d θ/dt = – θ₀ 2π sin 2πt

At t = 1/6, that is when θ = θ₀/2

d θ/dt = – θ₀π√3

v/l = – θ₀π√3

v = -θ₀π√3l

θ₀l [1/2 – π√6H/g] gives us the distance between the bob from A.